Highest Common Factor of 900, 552 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 900, 552 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 900, 552 is 12 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 900, 552 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 900, 552 is 12.
HCF(900, 552) = 12
HCF of 900, 552 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 900, 552 is 12.
Highest Common Factor of 900,552 is 12
Step 1: Since 900 > 552, we apply the division lemma to 900 and 552, to get
900 = 552 x 1 + 348
Step 2: Since the reminder 552 ≠ 0, we apply division lemma to 348 and 552, to get
552 = 348 x 1 + 204
Step 3: We consider the new divisor 348 and the new remainder 204, and apply the division lemma to get
348 = 204 x 1 + 144
We consider the new divisor 204 and the new remainder 144,and apply the division lemma to get
204 = 144 x 1 + 60
We consider the new divisor 144 and the new remainder 60,and apply the division lemma to get
144 = 60 x 2 + 24
We consider the new divisor 60 and the new remainder 24,and apply the division lemma to get
60 = 24 x 2 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 900 and 552 is 12
Notice that 12 = HCF(24,12) = HCF(60,24) = HCF(144,60) = HCF(204,144) = HCF(348,204) = HCF(552,348) = HCF(900,552) .
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Frequently Asked Questions on HCF of 900, 552 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 900, 552?
Answer: HCF of 900, 552 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 900, 552 using Euclid's Algorithm?
Answer: For arbitrary numbers 900, 552 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.